Question

plant,
ontract
Economic Order Quantity
6. The annual demand for an item is 3,200 units. Its unit cost is Rs. 6 and inventory
carrying cost per unit per year is 25% of unit cost. If the cost of one procurement
is Rs. 150, determine (1) Economic Order Quantity, (2) Number of orders in a year
and (3) Time lag between two consecutive orders.
Ans. (1) 800 units, (2) 4, (3) 3 months.
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amples​

Answer 1

(1) EOQ (Economic Order Quantity) = 800 units

(2) No of orders in year = 4

(3) Time between two consecutive order = 3 months

Given :

• Annual demand (D) = 3,200 units

• Cost of one order (S) = Rs. 150

• Cost per unit (C) = Rs. 6

• Holding Cost in % (I) = 25%

• Holding Cost in Rs. (H) = I × C

To find :

• Calculate EOQ (Economic Order Quantity) = Q

• No of orders per year

• Time between two consecutive order

Solution :

Holding Cost (H) = I × C

$\longrightarrow{\sf{6 \times \dfrac{25}{100}}}$

$\longrightarrow \:  1.5$

Holding Cost (H) = 1.5

★(1) Economic Order Quantity (EOQ) :

EOQ =

$\sf{\longrightarrow{Q={\sqrt{ \dfrac{2SD}{H}}}}}$

$\sf{\longrightarrow{Q={\sqrt{ \dfrac{2 \: \times \: 150 \: \times \: 3,200 }{1.5}}}}}$

$\sf{\longrightarrow{Q={\sqrt{\dfrac{9,60,000}{1.5}}}}}$

$\sf{\longrightarrow{Q={\sqrt{6,40,000}}}}$

$\longrightarrow Q = 800 \: units$

EOQ (Economic Order Quantity) = 800 units

___________________________

★ (2) Number of orders in a year :

$\sf{\longrightarrow{\dfrac{Annual \: demand }{EOQ}}}$

$\sf{\longrightarrow{\dfrac{3200}{800} \: = \: 4}}$

No of orders per year  =  4

___________________________

★ (3) Time between two consecutive order :

$\sf{\longrightarrow{\dfrac{EOQ }{Annual \: demand} \times \: Time}}$

$\sf{\longrightarrow{\dfrac{800}{3200} \times \: 12 \: = \: 3}}$

Time between two consecutive order = 3 months

Therefore,

EOQ (Economic Order Quantity) = 800 units

No of orders per year = 4

Time between two consecutive order = 3 months